In a welding process, a first part and a second part to be welded together at least locally receive a heat input in a welding zone to locally melt the parts. In this process, only a relatively small volume of the parts is heated to a high temperature, and thereafter rapidly cools. There has been limited capability so far to increase the weldability and quality of the weld during the welding in narrow-gap geometry, e.g. to reduce the chance for cracks, to lower porosity and lack of fusion during welding. Moreover the capabilities have been limited to positively change the mechanical properties of the weld joint and to increase the welding speed/deposition-rate. In previous attempts the metal parts are welded together by the laser beam with the formation of a weld seam. A heat treatment of the weld seam is provided through additional source along with laser beam as first source. These methods are intended to cancel out structural changes of the material of the metal parts again due to the welding thereof in the region of the weld seam infusing solidification defects such as cracks, pores and lack of fusion together.